Control of nonlinear time-varying systems

Necessary and sufficient conditions are given for a time-varying nonlinear system of specific form to be transformed into a time-invariant controllable linear system. Since the present work will be in a neighborhood of the origin, it is unnecessary to name specific sets and it is assumed that all assumptions, conditions and results hold in an open set in the appropriate Euclidean space that contains the origin. This theory can be combined with the global inverse function theorems to produce global results.